1. Field of the Invention
This invention relates to an open resonator for electromagnetic waves and more particularly to an open resonator formed by two concave spherical reflectors or one spherical and one plane reflector and applicable to electromagnetic waves of a frequency equal to or higher than the frequency of microwaves, which enables realization of a high Q value, a high excitation efficiency of the resonator mode and, when necessary, adjustment of the Q value, these features being achieved by taking advantage of the fact that a surface constituted of parallel stripes of a metal (or superconductor) having high electrical conductivity exhibits strong reflection characteristics with respect to polarized electromagnetic waves having an electric field parallel to the stripes and that very weak coupling of the electromagnetic waves through the grid surface established at the center portion of each mirror can be selectively adjusted by varying the width of the metal (or superconductor) stripes, the intervals between the stripes and the dimensional ratio of these to the wavelength.
2. Prior Art Statement
An ideal, loss-free resonator would be able to store the energy of an electromagnetic wave that enters it by maintaining the wave in a state of perpetual oscillation. Attempts have been made to apply the principle of resonators to precision measurement of ultra-low loss materials and to high-sensitivity detection of trace components in the atmosphere. In fact, however, existing resonators are not loss free and, therefore, the electromagnetic energy stored in the resonator decreases with the passage of time. The amount of electromagnetic energy dissipated per unit time in a resonator at any given time is proportional to the amount of energy stored in the resonator at that time. For evaluating a resonator, therefore, there is usually used a quality factor referred to as the Q value which is obtained by dividing the product of the angular frequency of the electromagnetic wave and the energy stored in the resonator by the energy dissipated per second in the resonator at the instant concerned. In the case where electromagnetic energy in the resonator is accumulated by the constant energy flow through the coupling with an electromagnetic wave, the electromagnetic energy stored in the resonator becomes saturated at the time the energy being dissipated therefrom becomes equal to the energy of the electromagnetic wave being supplied thereto, whereafter the energy stored in the resonator remains constant. Therefore, the lower the loss of the resonator, the greater is the amount of energy that can be stored therein. Thus a resonator with low loss has a large Q value. If it should be possible to control the resonator loss, it would be possible to set the resonance characteristics at the required Q value.
FIGS. 1 to 3 show examples of conventionally used optical resonators and FIGS. 4(a) and 4(b) show examples of waveguide-coupled millimeter-wave resonators. These will be explained first.
FIG. 1 illustrates an open resonator constituted of two plane partially-transparent mirrors disposed in parallel. When a plane wave 1 impinges on the plane partially-transparent mirror 3 on the incidence side, a part of the electromagnetic energy of the incident plane wave 1 enters the region between the parallelly placed plane mirrors 3 and 4, and is thus superimposed on itself by being repeatedly reflected back and forth between the two mirrors. The energy 5 is stored in the resonator most efficiently when the frequency of the incident wave is equal to the resonant frequency determined by the distance between the plane mirrors 3 and 4. In this case, as a result of the interference between the repeatedly reflected waves, the excitation efficiency of the open resonator with the incident wave 1 becomes maximum, whereby the amount of energy 5 stored in the resonator also becomes maximum. As a result, the energy flowing rate of the transmitted plane wave 2 likewise becomes maximum.
In the case of an open resonator using an incident beam of a finite beam diameter, as shown in FIG. 1, the plane parallel to the resonator suffers from two major disadvantages which prevent the resonator from having a high Q value. Namely, (1) the diffraction loss increases at the reflector edges and makes a precise theoretical knowledge of field distribution more difficult and (2) precise alignment is required.
Replacement of at least one of the plane reflectors by a concave reflector is advantageous in focusing the field into a small volume. Therefore, if apertures of the reflectors are large enough to render field intensities at their rims negligible, the diffraction loss becomes negligible and parallelism between the reflectors is not strictly required.
As shown in FIG. 2, if one or both of the partially-transparent mirrors 3' and 4' have concave spherical surfaces, an advantage of calculability without resorting to sophisticated computational techniques can be additionally obtained. In this case, the orthogonal modes prove to be the well-known Gaussian beam modes which are found in laser and maser cavities. Part of the incident beam 1 passes through the spherical partially-transparent mirror 3', whereby coupling is realized. When the frequency of the incident beam 1 is equal to a resonant frequency of the resonator, the energy 5 stored in the resonator becomes maximum as does the electromagnetic energy flow of the transmitted beam 2.
FIG. 3 shows a spherical mirror type open resonator having two spherical mirrors 6 and 7 with respective coupling holes 8 and 9 at the centers thereof. The spherical mirrors 6 and 7 are placed so as to form a resonant structure. The electromagnetic energy of the incident beam 1 transmits through the coupling hole 8 of the spherical mirror 6 into the resonator preformed with the two mirrors 6 and 7, whereby coupling is realized. When the frequency of the beam 1 is equal to a resonant frequency of the resonator, the energy flow of the transmitted beam 2 becomes maximum.
FIGS. 4(a) and 4(b) show conventional waveguide-coupled millimeter-wave resonators. In FIG. 4(a), a spherical mirror 6 and a plane mirror 7' are placed so as to form a resonant structure. Two small coupling holes 8 and 9 fabricated near the center of the spherical mirror 6 are used to transmit the energy to and from the input and output waveguide, in which input energy 11 and output energy 12 propagate. An input energy 11 is transmitted through the coupling hole 8 of the spherical mirror 6 into the resonator and the component thereof reflected in the axial direction by the plane mirror 7' facing the spherical mirror 6 is thus superimposed on itself by being repeatedly reflected between the two mirrors. The energy 5' stored in the resonator increases, causing the output energy 12 transmitting through the coupling hole 9 to increase. When the total energy dissipated per unit time in the resonator becomes equal to the energy flow rate into the resonator mode, a state of equilibrium is reached.
FIG. 4(b) shows an example in which the plane mirror 7' of the resonator of FIG. 4(a) is replaced with a spherical mirror 7 having a small coupling hole 9. The operation of this resonator is substantially the same as that of FIG. 4(a).
With the arrangements of the conventional open resonators shown in FIGS. 1 to 4, it is extremely difficult to control the loss of the resonator so as to obtain the desired Q value. Adjustment of the coupling strength of a resonator with a high Q value has been particularly difficult because the loss is set at a very weak level in such resonators, which makes it necessary to control the coupling strength under conditions of a weak coupling strength, which has been virtually impossible because of the limitations of fabrication technology.
Attachment of partially-transparent metallic thin films 13 as shown in FIG. 5(a) on the opposed surfaces on the mirrors 3 and 4 and 3' and 4' of FIG. 1 or FIG. 2 has also been adopted in place of the formation of the coupling hole in the mirror as shown in FIG. 4. In this case, a partially-transparent metallic thin film 13 is formed to have a small-transparency characteristic and a high-reflection characteristic by adjusting the thickness, etc., of the thin film. Furthermore, use of a latticed metallic film 14 of FIG. 5(b) or a porous metallic film 15 of FIG. 5(c) in place of the partially-transparent metallic thin film 13 of FIG. 5(a) has been proposed. The transparency and reflection characteristics are adjusted by varying the pattern in the case of FIG. 5(b) and by varying the void content in the case of FIG. 5(c).
With these films, however, it is very difficult to selectively control the reflection to become very high and the transparency to become very small. Particularly, the transparency varies depending on slight difference in thickness or pattern of a film and, therefore, it is very difficult to obtain films with the same degrees of reflection and transparency characteristics with high reproducibility.
The coupling holes 8 and 9 in the mirrors 6 and 7 should preferably be of large diameter for effective introduction of the input energy 1 or 11 into the resonator. However, for realizing a resonator with a high Q value it becomes necessary to make the coupling strength exceptionally weak. Thus the diameter of the coupling hole is usually made smaller than the wavelength. In the case of microwaves of a low frequency below 10 GHz, adjustment of the coupling strength is relatively easy from a technical point of view because the wavelength is long.
However, in the case of 2-3 mm electromagnetic waves, differences in fabrication precision or in the manner in which the surfaces are finished have a great effect on the distribution of the electric field of the high frequency waves, making it impracticable to achieve the subtle control of the coupling strength required in an open resonator at the millimeter and submillimeter wave frequencies.
For realizing a resonator with a high Q value, in addition to establishing a very weak coupling between the inside and outside of the resonator, it is also important to take into consideration how the resonator excitation signal can be efficiently converted into the resonator mode. How the conversion loss during resonator mode excitation varies depending on the coupling method will now be explained with reference to FIG. 6.
As shown in FIG. 6(a), the highest efficiency is obtained in the case of the open resonator constituted using a spherical partially-transparent mirror as denoted by reference numeral 16. By conducting the excitation using a signal beam which has been adjusted to a beam 17 that is very close to the mode 18 in the resonator, the beam 17 can be converted to the resonator mode 18 with high efficiency. On the other hand, as shown in FIG. 6(b), in the case of an open resonator constituted of two spherical mirrors 19 having respective very small coupling holes 20, at the time the converged incident beam 17 passes into the resonator through one of the small coupling holes 20 it is strongly diffracted and is diffused within the resonator at a large solid angle. However, of the coupled wave, only the component 21 traveling substantially in the direction of the optical axis is stored as the energy of resonator mode TEMooq, and most of the electromagnetic energy 24 escapes to the outside of the open resonator. The situation is exactly the same in the case of the waveguide-coupled open resonators with small coupling holes shown in FIGS. 4(a) and 4(b), and it is a major defect of these resonators that this conversion loss comes on top of and is added directly to the transmission loss of the resonator.
FIG. 14 is a graph corresponding to the case where a plane wave enters an open resonator according to FIG. 1 which is constituted of loss-free parallel plane mirrors and exhibits the transmission characteristics of an ideal Fabry-Perot resonator in which the diffraction loss, resistive loss at the mirror surfaces and the scattering loss are negligible. Where the incident wave is an electromagnetic wave of a finite beam diameter, this corresponds to the case of carrying out ideal conversion to resonator mode of an incident beam such as that in FIG. 6(a) in the open resonator of FIG. 2 which uses spherical partially-transparent mirrors in place of plane mirrors for avoiding diffraction loss or in an open resonator wherein one of the spherical mirrors is replaced with a plane mirror placed at the center of the two spherical mirrors.
In the graph of FIG. 14, the transmittance for different reflectances R of the mirrors indicating the ratio of signal power P2 of the transmitted electromagnetic wave to the signal power P1 of the incident electromagnetic wave is represented on the vertical axis and the phase difference .delta. caused by passage back and forth between the mirrors is represented on the horizontal axis. When this phase difference .delta. becomes equal to an integral multiple of 2.pi., i.e. when the difference in the length of the optical paths becomes equal to an integral multiple of the wavelength, resonance occurs and the transmittance P2/P1 assumes the maximum value 1. The sharpness of the resonance increases as the reflectance R of the mirrors becomes higher, making it possible to obtain a large Q value, while the maximum value of the transmittance is constant. When the phase difference .delta. is not equal to an integral multiple of 2.pi., the transmittance P2/P1 decreases with the increase in surface reflectance R. However, in actual practice, because of the finite loss in the resonator, the transmittance decreases gradually at higher Q values.
FIG. 15 is a schematic representation of the actual transmission characteristics of a millimeter wave open resonator with small coupling holes. As shown in FIG. 15, the sharpness of the resonance increases as the coupling hole of the mirror becomes smaller, making it possible to obtain a large Q value, while the maximum value of the transmittance P2/P1 is considerably reduced. At microwave frequency or millimeter wave frequency of several tens of GHz, sharp resonance, i.e. a high Q value, can be obtained by making the diameter of the coupling holes small. However, the high Q value achieved by this method is obtained at the expense of a large reduction in the excitation efficiency of the resonator, making it difficult to realize an S/N ratio on the order required for precision measurement using an open resonator with a very high Q value.
While the waveguide-coupled open resonator is the only type used for millimeter waves below the range of several tens of GHz, a high Q open resonator with very small coupling holes usually has large transmission loss of 20 to 30 dB. Most of the input signal power is lost to the outside of the resonator.
Open resonator technology is applied in conjunction with laser resonators for a broad range of wavelengths extending from light to microwaves, as well as in conjunction with scanning Fabry-Perot wavelength meters and widely in the field of spectrometry in connection with bandpass filters. Moreover, as this technology can enable the realization of resonators for use in the millimeter and sub-millimeter wave regions, it is also used in precision measurement of ultra-low loss materials and trace substances.
Generally speaking, variation of the resonant frequency of an open resonator can be easily realized by changing the distance between the mirror surfaces. However, it has not been possible to vary the Q value. The realization of an open resonator which, in addition to being variable in its resonant frequency characteristics, also allows free selection of its Q value over a wide range would provide many practical advantages.